Generalizing Fisher's "reproductive value": linear differential and difference equations of "dilute" biological systems.

Abstract:

:R. A. Fisher's 1930 "reproductive value" is defined as the contribution made by a population's initial age elements to its asymptotically dominating exponential growth mode. For the Leslie discrete-time model, it is the characteristic row vector of the Leslie matrix, and for the integral-equation model of Lotka the similar eigenfunction. It generalizes neatly to a 2-sex model of linear differential equations, and to general n-variable linear systems. However, when resource limitations end the "dilute" stage of linearity, reproductive value loses positive definability. The present linear analysis prepares the way for generalizing reproductive value to nonlinear systems involving first-degree-homogeneous relationships.

authors

Samuelson PA

doi

10.1073/pnas.74.11.5189

subject

Has Abstract

pub_date

1977-11-01 00:00:00

pages

5189-92

issue

11

eissn

0027-8424

issn

1091-6490

journal_volume

74

pub_type

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